Let us make an in-depth study of the embodiment of technological progress in macro economic

Technological progress was introduced into the preceding analysis in the simplest possible way—as a factor completely independent of the capital stock growth rate and the labour force growth rate.

This amounts to viewing technological progress as know-how which falls like manna from heaven and applies equally and impartially to all units of the economy’s labour force and capital stock.

Such technological progress—for example, organizational improvements—is formally described as disembodied, because it yields its benefits without the necessity of embodiment in newly produced capital goods or newly trained workers. As long as technological progress is disembodied, we may assume in theory that the labour force is homogeneous, because the productivity of all workers, regardless of age, training, or education, will benefit proportionally from technological progress.


Similarly, we may assume that all units of capital are homogeneous because all units of capital, regardless of age and design, will benefit proportionality from technological progress. By contrast, embodied technological progress must be physically incorporated in newly produced capital goods or newly trained workers before it can contribute to the rate of growth of the economy’s output. (For example, jet engines required embodiment in newly produced capital goods, namely, jet airplanes). Capital can then no longer be assumed to be homogeneous.

The capital stock becomes a mixed stock of different “vintages.” Because they embody more technological progress, newer machines are more productive than older ones. Similarly, the labour force can no longer be assumed to be homogeneous. Like units of the capital stock, different individuals in the labour force are distinguished by age and training or education. Individuals of the different vintage are then more productive than individuals of earlier vintages.

Although embodied technological advances refer to those that are embodied in either the capital stock or the labour force—that is, in “physical capital” or “human capital”—in what follows we will limit attention to technological advance of a kind that either is or is not embodied in physical capital. Advances of this kind have been described as “design” or “organizational” the former requiring new capital goods and the latter requiring only new procedures or methods.

Economists working in this area disagree as to what part of actual technological advance is design and what part is organizational. If it is true, as some argue, that the larger part is of a design nature that must be embodied in new capital goods if its benefits are to be gained, then it also appears true that the real importance of the capital stock cannot be indicated merely by the fraction of the growth rate of output that is directly explained by the growth rate of the physical stock of capital.


Its real importance is much greater, because the capital stock is the vehicle through which technological progress is worked into the production process and without which the growth rate of output would be only a fraction of what it actually is. From this point of view, the capital stock, which otherwise could be downgraded to a minor role, reassumes the position of primacy that most people always thought it occupied.

A numerical illustration will clarify the difference between the earlier approach, in which technological advance was assumed to be completely disembodied, and the present approach, in which it is in part embodied. We assume an economy in which the capital stock is equally divided into one-year through twenty-year vintages.

All capital goods last exactly twenty years, so at the end of each year the capital goods then of twenty-year vintage come up for replacement. This will be 5 percent of the capital stock. We also assume that gross investment is equal to replacement investment—that is, net investment is zero. This means that each year’s gross investment is equal to 5 percent of the capital stock, which in turn is a physical stock that does not change in amount from year to year.

Some part of the economy’s technological advance is embodied in newly produced capital goods. Assume that technological advance-is such that the capital goods produced each year show a 3.5 percent quality improvement, or productivity increase, over the capital goods produced during the preceding year. Any variable that grows at a 3.5 percent compound rate per annum will double in size in twenty years.


Therefore, a capital good newly produced in Year t and embodying the improvements of Year t and all preceding years will have twice the productivity of the capital good of Year t- 20 that it replaces. The comparison is, of course, between capital goods of equal real cost; the physical makeup of the old and the new may be completely different. Because gross investment is by assumption equal to replacement investment and because replacement is understood to be the amount of capital goods that must be produced during the period in order to maintain the total capital stock, we appear to have a case of zero growth rate in the capital stock.

However, even though each unit of capital is replaced at the end of twenty years by another unit of equal real cost, the replacement unit is twice as productive as the replaced unit and therefore in effect is equivalent in real terms to two of the replaced units. For example, if the total capital stock is thought of as 100 units, this year’s gross investment of 5 units for replacement equals the 5 units that wear out during this year and keeps the total capital stock unchanged at 100 units; but, because the 5 replacement units are equivalent in productivity to 10 of the replaced units, in effect the capital stock has been enlarged from 100 to 105 units.

In our simple case, this increase would not be revealed to the statistician who measured merely the number of units or the physical quantity of capital. An increase in the capital stock is nonetheless there but not in explicit form. In the present example, this implicit, or effective, increase of 5 in the capital stock indicates a 5 percent growth rate (∆K/K= 5/100 = 5 percent).

Otherwise viewed, gross investment that is equal to replacement—that is, to 5 percent of the capital stock—is effectively gross investment equal to 10 percent of the capital stock, one half of which is 5 percent for replacement and the other half of which is, in effect, 5 percent for net investment.

On the basis of all the preceding assumptions and if we now add the final assumption that b equals 0.25, we find that the part of technological advance that is embodied in the capital stock accounts for 0, 25 (5/100), or about 1.2 percentage points of the rate of output growth. This figure of 1.2 is derived from a whole series of assumptions, some quite arbitrary, and is likely to be far wide of the true figure that is unknown. Nonetheless, even if the actual figure is well above or below 1.2, we still reach conclusions quite different from those reached in the earlier discussion in which technological advance was completely disembodied.

Without knowing what the correct figure really is, many economists still feel, on the basis of available evidence, that the contribution of the capital stock to the rate of output growth comes in large part, if not primarily, from the role of capital as a vehicle for the embodiment of technological advance. There is, in sum, much more to the role of the capital stock in the growth process than the mere growth in the quantity of capital goods.

Although we choose to limit attention in this section to the question of the embodiment of technological advance in physical capital, the embodiment of technological advance in “human capital” involves a parallel analysis.

Just as the mere growth in the quantity of physical capital accounts for part of the growth of output, so the mere growth in the quantity of human capital does the same. But, as in case of the capital stock, over and above the mere growth in the amount of labour input is the question of the improvement in the quality as the result of the embodiment of education and training in people It may well be that this is a more important factor in explaining the growth rate of output than is the embodiment of technological advance in the capital stock.